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hram777 [196]
2 years ago
5

Work out the gradient of the straight line that passes through (2,6) and (6,12)

Mathematics
1 answer:
Furkat [3]2 years ago
5 0

Answer:

The gradient of the straight line that passes through (2, 6) and (6, 12) is m = \frac{3}{2}.

Step-by-step explanation:

Mathematically speaking, lines are represented by following first-order polynomials of the form:

y = b + m\cdot x (1)

Where:

x - Independent variable.

y - Dependent variable.

m - Slope.

b - Intercept.

The gradient of the function is represented by the first derivative of the function:

y' = m

Then, we conclude that the gradient of the staight line is the slope. According to Euclidean Geometry, a line can be form after knowing the locations of two distinct points on plane. By definition of secant line, we calculate the slope:

m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}} (2)

Where:

x_{A}, y_{A} - Coordinates of point A.

x_{B}, y_{B} - Coordinates of point B.

If we know that A(x,y) = (2,6) and B(x,y) = (6,12), then the gradient of the straight line is:

m = \frac{12-6}{6-2}

m = \frac{6}{4}

m = \frac{3}{2}

The gradient of the straight line that passes through (2, 6) and (6, 12) is m = \frac{3}{2}.

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Picture:

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